In this section, we extend a few results on BB steps to the TBB step with the choices for the target \(\tau _k\)  described in Sections REF  and REF . Global convergence of the gradient method with BB steps has been proven by Raydan [1]} for strictly convex quadratic functions. Dai and Liao [2]} and Dai [3]} show R-linear convergence of the method for a class of BB stepsizes. We follow [3]} and [2]} to extend the results to the TBB steps.
